A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative

Abstract

In this article, we proposed a compact difference-Galerkin spectral method for the fourth-order equation in multi-dimensional space with the time-fractional derivative order α∈(1,2). The novel compact difference-Galerkin spectral method can effectively address the issue of high-order derivative accuracy and handle complex boundary problems. Simultaneously, the main conclusions of this article, including the stability, convergence, and solvability of the method, are derived. Finally, some computational experiments are illustrated to demonstrate the superiority of the compact difference-Galerkin spectral method.

Keywords

• Galerkin spectral method
• time-fractional order
• variable coefficient fourth-order equation